Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, , 50 - 61, 05.07.2018
https://doi.org/10.24330/ieja.440192

Öz

Kaynakça

  • N. Bourbaki, Algebra II, Chapters 4-7, Springer-Verlag, Berlin-Heidelberg, 2003.
  • R. C. Daileda, A non-UFD integral domains in which irreducibles are prime, preprint. http://ramanujan.math.trinity.edu/rdaileda/teach/m4363s07/non_ufd.pdf.
  • N. J. Fine, Binomial coecients modulo a prime, Amer. Math. Monthly, 54 (1947), 589-592.
  • L. Fuchs, In nite Abelian Groups, Vol. II, Pure and Applied Mathematics, Vol. 36-II, Academic Press, New York-London, 1973.
  • R. Gilmer, Commutative Semigroup Rings, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1984.
  • R. Gilmer, Property E in commutative monoid rings, Group and semigroup rings (Johannesburg, 1985), North-Holland Math. Stud., 126, Notas Mat., 111, North-Holland, Amsterdam, (1986), 13-18.
  • R. Gipson and H. Kulosman, Atomic and AP semigroup rings F[X;M], where M is a submonoid of the additive monoid of nonnegative rational numbers, Int. Electron. J. Algebra, 22 (2017), 133-146.
  • T. Y. Lam and K. H. Leung, On vanishing sums of roots of unity, J. Algebra, 224(1) (2000), 91-109.
  • R. Matsuda, On algebraic properties of in nite group rings, Bull. Fac. Sci. Ibaraki Univ. Ser. A, 7 (1975), 29-37.
  • D. G. Northcott, Lessons on Rings, Modules and Multiplicities, Cambridge University Press, London, 1968.

IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS

Yıl 2018, , 50 - 61, 05.07.2018
https://doi.org/10.24330/ieja.440192

Öz

We extend a lemma by Matsuda about the irreducibility of the
binomial X 􀀀 1 in the semigroup ring F[X;G], where F is a eld, G is an
abelian torsion-free group and is an element of G of height (0; 0; 0; : : : ).
In our extension, G is replaced by any submonoid of (Q+; +). The eld F,
however, has to be of characteristic 0. We give an application of our main
result.

Kaynakça

  • N. Bourbaki, Algebra II, Chapters 4-7, Springer-Verlag, Berlin-Heidelberg, 2003.
  • R. C. Daileda, A non-UFD integral domains in which irreducibles are prime, preprint. http://ramanujan.math.trinity.edu/rdaileda/teach/m4363s07/non_ufd.pdf.
  • N. J. Fine, Binomial coecients modulo a prime, Amer. Math. Monthly, 54 (1947), 589-592.
  • L. Fuchs, In nite Abelian Groups, Vol. II, Pure and Applied Mathematics, Vol. 36-II, Academic Press, New York-London, 1973.
  • R. Gilmer, Commutative Semigroup Rings, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1984.
  • R. Gilmer, Property E in commutative monoid rings, Group and semigroup rings (Johannesburg, 1985), North-Holland Math. Stud., 126, Notas Mat., 111, North-Holland, Amsterdam, (1986), 13-18.
  • R. Gipson and H. Kulosman, Atomic and AP semigroup rings F[X;M], where M is a submonoid of the additive monoid of nonnegative rational numbers, Int. Electron. J. Algebra, 22 (2017), 133-146.
  • T. Y. Lam and K. H. Leung, On vanishing sums of roots of unity, J. Algebra, 224(1) (2000), 91-109.
  • R. Matsuda, On algebraic properties of in nite group rings, Bull. Fac. Sci. Ibaraki Univ. Ser. A, 7 (1975), 29-37.
  • D. G. Northcott, Lessons on Rings, Modules and Multiplicities, Cambridge University Press, London, 1968.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Katie Christensen Bu kişi benim

Ryan Gipson Bu kişi benim

Hamid Kulosman Bu kişi benim

Yayımlanma Tarihi 5 Temmuz 2018
Yayımlandığı Sayı Yıl 2018

Kaynak Göster

APA Christensen, K., Gipson, R., & Kulosman, H. (2018). IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. International Electronic Journal of Algebra, 24(24), 50-61. https://doi.org/10.24330/ieja.440192
AMA Christensen K, Gipson R, Kulosman H. IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. IEJA. Temmuz 2018;24(24):50-61. doi:10.24330/ieja.440192
Chicago Christensen, Katie, Ryan Gipson, ve Hamid Kulosman. “IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS”. International Electronic Journal of Algebra 24, sy. 24 (Temmuz 2018): 50-61. https://doi.org/10.24330/ieja.440192.
EndNote Christensen K, Gipson R, Kulosman H (01 Temmuz 2018) IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. International Electronic Journal of Algebra 24 24 50–61.
IEEE K. Christensen, R. Gipson, ve H. Kulosman, “IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS”, IEJA, c. 24, sy. 24, ss. 50–61, 2018, doi: 10.24330/ieja.440192.
ISNAD Christensen, Katie vd. “IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS”. International Electronic Journal of Algebra 24/24 (Temmuz 2018), 50-61. https://doi.org/10.24330/ieja.440192.
JAMA Christensen K, Gipson R, Kulosman H. IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. IEJA. 2018;24:50–61.
MLA Christensen, Katie vd. “IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS”. International Electronic Journal of Algebra, c. 24, sy. 24, 2018, ss. 50-61, doi:10.24330/ieja.440192.
Vancouver Christensen K, Gipson R, Kulosman H. IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. IEJA. 2018;24(24):50-61.